For a question such as this one, the answer has to be an imprecise answer, because we do not have any direct evidence of dinosaurs having lived in Binghamton.
I say that we have no direct evidence, because we do not have rocks of Mesozoic age (when the dinosaurs lived) in the Binghamton area. However, we do have rocks of early Mesozoic (Triassic) age in northern New Jersey and the southern Hudson Valley, and fossil footprints of dinosaurs have been found in these rocks. The rocks in question formed in ancient lakes and surrounding swampy areas during the Triassic and early Jurassic Periods of the Mesozoic Era (Time of Intermediate Life.)
These environments have been compared with the lakes formed within the African Rift Valleys in modern day Kenya, Tanzania and other countries. Probably these rift valleys in modern New Jersey, Pennsylvania and Connecticut had climates in the Triassic that were similar to East Africa today, and sediments around lakes dried out from time to time. The mud with dinosaur footprints were buried by other sediments and changed through time from sediments to sedimentary rocks, some with fossil traces of the dinosaur feet.
The only dinosaur fossils known from New York state are the footprints found in these Triassic mud-stones from southern New York, near the New Jersey border. The fossil footprints or tracks are thought to have been made by Coelophysis, a Triassic dinosaur that walked on its hind legs, thus bipedal.
So, the question seems to be, if there are fossils found downstate that are direct evidence of dinosaurs having lived in New York State, near the New Jersey border, does that mean that some of these dinosaurs might have wandered over our way, and thus lived briefly here in the Binghamton area? Probably so, because these reptiles are known to have migrated hundreds of miles or more in search of food, and I at least would like to think that, yes, there were likely some Binghamton dinosaurs, even if only temporary residents.
If you are interested in learning more about these fascinating guys, there is an excellent exhibit on them in the Museum of the Earth (M.O.T.E.) in Ithaca, on Trumansburg Road on the west side of Cayuga Lake. There are even fossils of their footprints in the collections there, truly evidence of New York dinosaurs. Ask your parents or teacher to arrange a visit